Small Into-Isomorphisms Between Spaces of Continuous Functions

Isomorphisms between Spaces of Vector-valued Continuous Functions

A theorem due to Milutin [12] (see also [13]) asserts that for any two uncountable compact metric spaces Qt and Q2> t n e spaces of continuous real-valued functions C ^ ) and C(Q2) are linearly isomorphic. It immediately follows from consideration of tensor products that if X is any Banach space then QQ^X) and C(Q2;X) are isomorphic. The purpose of this paper is to show that this conclusion is ...

Weight-preserving isomorphisms between spaces of continuous functions: The scalar case

Let F be a finite field and let A and B be vector spaces of F-valued continuous functions defined on locally compact spaces X and Y , respectively. We look at the representation of linear bijections H : A −→ B by continuous functions h : Y −→ X as weighted composition operators. In order to do it, we extend the notion of Hamming metric to infinite spaces. Our main result establishes that under ...

Isomorphisms of Spaces of Continuous Affine Functions on Compact Convex Sets with Lindelöf Boundaries

Let X, Y be compact convex sets such that every extreme point of X and Y is a weak peak point and both extX and extY are Lindelöf spaces. We prove that, if there exists an isomorphism T : Ac(X) → Ac(Y ) with ‖T‖ · ‖T‖ < 2, then extX is homeomorphic to extY . This generalizes results of H.B. Cohen and C.H. Chu.

Spaces of Continuous Functions

Let X be a completely regular topological space, B(X) the Banach space of real-valued bounded continuous functions on X, with the usual norm ||&|| =supa?£x|&(#)| • A subset GCB(X) is called completely regular (c.r.) over X if given any closed subset KQ.X and point XoÇzX — K, there exists a ô £ G such that &(#o) = |NI a n ( i sup^^is: \b(x)\ <||&||. A topological space X is completely regular in...

Spaces of continuous functions into a Banach space